1. Field of the Invention
The present invention relates to a method and arrangement of generating a non-diffractive beam (viz., so-called Bessel beam) at a location which is remote from a Bessel beam producing optical means. Further, the present invention relates to an optical scanner for reading bar coded labels to which the above mentioned method is effectively applicable.
2. Description of the Prior Art
It was recently shown by Durnin that propagation-invariant sharply peaked solutions of the scalar wave equation exists, in an article entitled "Exact solutions for non-diffracting beams. I. The scalar theory", J. Opt. Soc. Am. A, Vol. 4, No. 4, April 1987, pages 651-654 (referred to as prior art paper 1). These solutions, called diffraction-free beams or Bessel beams, contain an infinite energy and accordingly, they are not experimentally realizable.
It has been, however, shown experimentally, also by Durnin, that finite-aperture approximations of these fields exhibit the main propagation features of true diffraction-free beams over a large depth of field, in an article entitled "Diffraction-Free Beams", Volume 58, Apr. 13, 1987, pages 1499-1501 (referred to as prior art paper 2).
On the other hand, Turunen et al have shown a modification of the arrangement in the above mentioned prior art paper 2, in an article entitled "Holographic generation of diffraction-free beams", Applied Optics, Vol. 27, No. 19, Oct. 1, 1988, pages 3959-3962 (referred to as prior art paper 3).
Further, Perez et al have disclosed generation of the Bessel beam employing an axicon in an article entitled "Diffraction patterns and zone plates produced by thin linear axicons", Optica Acta, 1986, Vol. 33,No. 9, pages 1161-1176 (referred to as prior art paper 4).
Before turning to the present invention it is deemed advantageous to briefly discuss the above mentioned prior art techniques with reference to FIGS. 1(a)-1(c) and 2(a)-2(c).
FIG. 1(a) shows an optics arrangement for generating a finite-aperture approximation of a Bessel beam, which wee shown in the above mentioned prior art papers 1 and 2, In FIG. 1(e), a coherent plane wave depicted by reference numeral 10 illuminates a thin annular slit 12, which is placed in the focal plane of a positive lens 14 ("F" denotes a focal length of the lens 14). The wavefront after the lens 14 is seen to be conical (i.e., the wave vectors are uniformly distributed on a cone). The prior art paper 1 shows that the arrangement shown in FIG. 1 exhibits a Bessel beam over a distance depicted by L1. A character "L" with a numeral is also used to depict a Bessel beam in addition to a distance.
FIGS. 2(a)-2(c) show the beam intensity profiles at z=25, 77 and 100 cm (z denotes an optical axis), respectively, with the intensity of the Gaussian profiles (depicted by broken lines) multiplied by a factor 10. It is understood that the Bessel beam has a remarkably greater depth of field than the Gaussian beam.
Turunen et al., disclosed, in the prior art paper 3, an arrangement shown In FIG. 1(b) using a holographic optical element (viz., a cylindrically symmetric hologram) 16. The FIG. 1(b) arrangement exhibits a Bessel beam L2 whose distance is twice L1 in FIG. 1(a). According to Turunen et al, the hologram 16 converts an incident plane wave 18 into a conical wave, which (according to geometrical optics) after the plane, at which the lens 14 is located, is similar to the wavefront in FIG. 1(a). Turunen et al., have shown that the diffraction-free propagation ranges a geometrical optics prediction of EQU L2=D.rho./.lambda. (1)
where D is a radius of the hologram 16, .rho. a pitch of the slit of the hologram 16, and .lambda. a wave length of the incoming coherent plane wave.
Further, Turunen et al., have described the full width of the bright central lobe (viz., diameter of a Bessel beam) W is represented by EQU W=0.766.rho. (2)
FIG. 1(c) shows another arrangement using an axicon 20 for generating a Bessel beam having a length L3, which has been shown in the above mentioned prior art paper 3.
For further details regarding the arrangements of FIGS. 1(a)-1(c), reference should be made to prior art papers 1-3 respectively.
As shown in FIG. 1(a), the Bessel beam exists over a distance L1 starting immediately after the lens 14. This applies to the he other arrangements shown in FIGS. 1(b) and 1(c). Accordingly, if each of these arrangements is applied to an optical device wherein a beam radius should be very small, each of the above mentioned prior art techniques may encounter the problem that there is insufficient room or space for accommodating an optical member(s) within the range within which the Bessel beam can be generated. In more specific terms, if the diameter of the Bessel beam (W) is 0.2 mm, then the pitch of the hologram slit (.rho.) is about 0.26 mm as will be appreciated from equation (2). Further, if the radius of the hologram 16 is 5 mm, then the Bessel beam length L2 becomes approximately 2 m.
Therefore as will be appreciated, if a beam having a very small radius (viz., a Bessel beam) is required to impinge an object beyond the Bessel beam, each of the above mentioned prior techniques is no longer utilized.